DOCSLIB.ORG

Scattering Length from Meson Decays C.W.Wong, UCLA

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Scattering Length from Meson Decays C.W.Wong, UCLA Problem solving and the scariest exam in the history of undergraduate education C.W.Wong, UCLA • Why problem solving? • Why the old Mathematical Tripos exam? • Why the falling chain of Hopkins, Tait, Steele and Cayley? • Why does it conserve energy? • Conclusions Kentucky, April 19, 2007 Why problem solving? • Keh-fei is a good problem solver • Scientific research = problem solving • Can problem solving be taught? Optimistically: Yes •How? by the right people (teachers, mentors, peers, students) in the right places (institutions, facilities) at the right times (post Industrial Revolution) • Case study: The scariest (most competitive) exam in the history of undergraduate education = the old Cambridge Mathematical Tripos exam, 1780-1909 Why the old Cambridge Mathematical Tripos exam? Model for written competitive exams in the English-speaking world Cambridge University: • 800th Anniversary in 2009 •81Nobel Prize winners worked or studied there, 1904-2005 • Isaac Newton studied and taught there: 1661-5, 1669-96 • Home of math. Physics in the 19th century: Clerk Maxwell studied and taught there: 1850-4, 1871-9 More about the Old Tripos (1): •Tripos= three-legged stool on which the moderator sat in the original oral disputative exam (“wrangling”) • Old Tripos, 1780-1909: Required only for passing with honors Written exam Graduates ranked in Order of Merit Wranglers = students passing with first-class honors: Senior Wrangler (SW) = top student Second Wrangler (2W) = second best student Wooden Spoon (WS) = last student passing with honors • 1820-1909: The old Tripos became increasingly competitive. More about the Old Tripos (2): • Lasting 2 weeks: 1st week: bookwork testing mastery of basic concepts, definitions, laws & proofs using Newton’s geometrical method 2nd week: problem papers often requiring new mathematical techniques applied to novel situations • Morning and afternoon exam papers, each usually 3 hours long: Each paper had 10-12 questions. Each question (15-18 minutes each) had several parts: theorem proof, simple application, difficult application. Usually all parts had to be answered correctly to score. • The 1881 Tripos: 18 three-hours papers with a total score of 33,541 marks: SW got 16,368 marks, 2W got 13,188, WS got 247. • Examiners believed that marks were proportionate to the abilities of the lower-placed candidates, but did not do full justice to the highest. Famous wranglers (1): Only five exceptional mathematicians: • J.J. Sylvester (2W, 1837) •A.Cayley(SW, 1842): wrote 967 papers, 1841-95 (Euler wrote only 800 papers) •W.K. Clifford (2W, 1867): Cayley’s first student • G.H. Hardy (4W, 1898): collaborated with Ramanujan • J.E. Littlewood (SW, 1905): collaborated with Hardy Famous wranglers (2): Many distinguished physicists thrived in the competitive atmosphere of Cambridge & the fellowship of the Royal Society: •G. Stokes (SW, 1841): fluid dynamics, optics • W. Thomson (Lord Kelvin) (2W, 1845): trans-Atlantic cable, thermodynamics, Kelvin temperature scale • J. Clerk Maxwell (2W, 1854): kinetic theory, Maxwell equations (Perhaps greatest physicist after Newton & Einstein) • J.W. Strutt (Lord Rayleigh) (SW, 1865): discovered argon; gases • J.J. Thomson (2W, 1880): discovered electron; electricity in gases • William Bragg (3W, 1884): X-ray crystallography Coaches of the old Tripos: Students prepared for the exam by taking private lessons from coaches. • Coach = tutor/trainer, named after the stagecoach (Oxford undergraduate slang, 1830’s) • Coach = closed carriage, named after the Hungarian village Kocs where this carriage originated • Cambridge Students learned to solve problems against the clock from their coaches. (Training in memory and mental discipline.) More about the Old Tripos (3): • Textbooks: were written directly or indirectly for students: Whewell (1823), Tait & Steele (1856), Routh (1898). •Collectionsof Tripos problems and solutions: Wright (1827-31), Wolstenholme (1867, 1878) and private collections of coaches • Tripos examiners: Always top Wranglers, usually young (within 4-8 years of graduation). Many were coaches. • The “arms race”, 1820-1909: Students were better prepared by coaches and by using textbooks and problem collections, but the problem papers became increasingly more difficult. 1828 Tripos: 4 days, 8 papers 1881 Tripos: 9 days, 18 papers • Tripos stress: Cakewalk: Cayley (SW, 1842), Rayleigh (SW, 1865) Had enough: Kelvin (2W, 1845) Nerves: Maxwell (2W, 1854), J.J. Thomson (2W, 1880) Nervous breakdown: James Wilson (SW, 1859) Could not walk 50 yards afterwards Took 3 months to recuperate & only by forgetting all Cambridge mathematics The modern math Tripos exams: • 1909: Order of merit was abandoned because more students avoided the math Tripos by taking the easier Tripos exams in other subjects. • Present-day Math. Tripos: 3 years for the BA degree: with four 3-hour papers per year (called Parts IA, IB and II) on different mixed subjects Tripos Part III taken in the 4th year: 6 long (9 short) courses, each with a 3-hour (2-hour) exam Why the falling chain of Hopkins, Tait, Steele and Cayley? Excessive respect for Newton’s methods retarded British mathematics and dynamics in the 18-19th centuries. It also caused mistakes in Tripos solutions: Example: Chain falls down link by link from a coil on a table. Incorrect energy-nonconserving (or inelastic) solution was given by coach William Hopkins, and published by • Tait and Steele (SW & 2W, 1854), 1856: First textbook on problem •Cayley(SW, 1842), 1857: First paper on problem • Wolstenholme (3W, 1850), 1878: Problem collection • Jeans (2W, 1880), 1907: Textbook •Lamb (4W, 1898), 1914: Textbook • Sommerfeld, Mechanik, 1943: Textbook • All the physics and engineering textbooks on mechanics that I have checked Mistakes in Tripos solutions: Surprising after scrutiny by generations of teachers, coaches and students • Hopkins: coached Stokes, Kelvin, Maxwellk, Tait, Todhunter • Cayley: Perhaps the best pure problem solver in 19th century Cambridge & the best mathematician of Victorian Britain • Sommerfeld: One of the best teachers of physics 4 Ph.D. students won Nobel Prizes: Pauli, Heisenberg, Debye, Bethe 2 postdocs won Nobel Prizes: Pauling, Rabi Correct energy-conserving (or elastic) solution has been given by • C.W. Wong and K. Yasui, 2006: First correct theoretical treatment • C.W. Wong, S.H. Youn and K. Yasui, 2007: First indirect experimental confirmation Why does it conserve energy? Mathematical picture: ρ x 2 Lagrangian: L(x,v) = xv 2 + ρ g 2 2 d (ρ xv) = ρ xa + ρv 2 Lagrange equation: dt ∂L s = = −ρ gx + ρv 2 ∂x 2 Solution: g ⎧g/3 ⎧0 inelastic, a = = ⎨ , if s = ⎨ 3−s ⎩g/2 ⎩1 elastic. Physical pictures Inelastic picture of Hopkins, Tait, Steele, Cayley and Sommerfeld: Falling link sticks to falling chain in a totally inelastic collision (Carnot’s theorem) Elastic picture of Wong and Yasui: Falling link gains energy when it breaks off from stationary chain segment. Falling link loses energy when it joins falling chain segment. The whole process is elastic. Conclusions: •Best problem solvers have innate abilities, but are influenced by people, places and times. Case study: Famous problem solvers who took the Math Tripos exam in Cambridge (home of Newton and Maxwell) in Maxwell’s time (right after the Industrial Revolution). • Original research is enhanced by fierce competition => The elite world of meritocracy, evolution, capitalism, politics. Lesson? To foster competition, only the best students should be graded A+. • Retention of learning is helped by rewards of pleasure => The feel-good world of democracy, socialism, Heaven (the Greatest Society) Lesson? To maximize pleasure & memory, every student should be graded A+. • Grading culture, begun in 19th century Cambridge, flourishes to this day. •The physics in this talk? There is a mistake in the accepted solutions of Tripos problems, after 150 years of careful scrutiny by generations of mathematicians and physicists..
Load more

Recommended publications
  • Guardiola Lusts for Football's Ultimate Dream Team
    TENNIS | Page 6 FOOTBALL | Page 4 Djokovic Record To Advertise here Call: 444 11 300, 444 66 621 vows to keep unbeaten run fi ghting to beckons for stay ahead leaders PSG Tuesday, February 2, 2016 CRICKET Rabia II 23, 1437 AH South Africa seek GULF TIMES redemption in One-day series SPORT Page 10 CYCLING FOOTBALL Dutch star Wild Guardiola to succeed back in Qatar, has Pellegrini at Worlds in mind Man City ‘It is good to see the course…you can feel a bit what kind of conditions would be here when we have the worlds here in October. We will also know where we have to improve’ By Yash Mudgal as the other girls I race against,” said Doha Hosking, who missed much of the end of last season with a hand injury. Hosking is looking forward to her re- irsten Wild is back in Doha turn to the top level of the peloton. “It’s after a gap of one year to sig- been a long time since I raced with the nal her World Champion- ‘big girls’ so I’m nervous to get back in Bayern Munich coach Pep Guardiola (L) reacts next to Manchester City man- ships ambitions. the international peloton,” the Aus- ager Manuel Pellegrini during their Champions League Group E soccer match KThe Dutch star Wild has spent the tralian said. in Manchester on November 25, 2014. winter taking part in track competi- “It’s always hard to know if what you tions, but is happy to be back in Doha have done over the winter – or sum- AFP “Out of respect for Manuel Pel- for her fi fth Ladies Tour of title.
    [Show full text]
  • Mullocks Specialist Auctioneers & Valuers
    The Clive Pavilion Mullocks Specialist Auctioneers & Valuers Ludlow Racecourse Bromfield Ludlow Two Day Sale of Sporting Memorabilia SY8 2BTY Started 15 Apr 2015 11:00 BST United Kingdom Lot Description Signed 1954 Joe Davis and Fred Davis snooker exhibition programme dated 11-12/03/1954 at T.A centre Rotherham, Joes Davis (20 1 years Undefeated Snooker Champion of the World) and Fred Davis (1954 Present Snooker Champion of the World) signed by both players VG example, t/w 1955 Cavalcade of Sport pro ...[more] 2 Snooker cue tipper in bamboo and brass in good condition c/w steel tip file 2x one piece snooker cues both weighing 17oz, both without tips, but complete with the original black japanned cue cases one with a 3 Burroughes and Watts transfer label Interesting half size Bagatelle wooden table top game folding table complete with numbered gate section, and a original cue, some 4 minor wear marks to cloth and wood, however still very playable, overall size 35 x 122cm – folded 60x 35cm Billiard Tokens – 7x brass billiard tokens embossed and inscribed to the border “Ilkeston Reliable Billiard Marker” – the purpose being 5 that players would “rent” the table for a time, receiving tokens in exchange for the amount paid. 1903 Sword Fencing white metal medal with a triumphant figure to the front and ‘Dem Vaterlande Unser Streßen’ and to the rear a 6 rampant Lion over the Swiss cross, surrounded by the words ‘Eidenössisches Turnfest 1903 in Zurich’ c/w small ribbon Royal Caledonian Curling Club white metal medal with an early embossed curling
    [Show full text]
  • Women in Math
    “The Woman Who Bested the Men at Math” Thus Fawcett’s triumph was astonishing—all the by Mike Dash more so when it is realized that Cambridge, like most of the other great universities of the day, including http://blogs.smithsonianmag.com/history/2011/10 Oxford, Harvard and Yale, did not admit women or /the-woman-who-bested-the-men-at-math/ permit them to take degrees. Separate colleges had been established for women only in the 1870s, and To be a woman in the Victorian age was to be weak: they gradually became loosely affiliated with the connection was that definite. To be female was universities. By the 1890s things had advanced to the also to be fragile, dependent, prone to nerves and— point where the women at those colleges— not least—possessed of a mind that was several Cambridge had two, Newnham and Girton—were degrees inferior to a man’s. For much of the 19th allowed to take the same exams as males. But they century, women were not expected to shine either were marked and ranked separately, with the academically or athletically, and those who women’s results read after the men’s at an annual attempted to do so were cautioned that they were ceremony held at the university Senate House. Math taking an appalling risk. Mainstream medicine was students, uniquely, were ranked in numerical order, clear on this point: to dream of studying at the from first to last, rather than in broad bands of university level was to chance madness or sterility, if ability, so it was possible to compare one student not both.
    [Show full text]
  • Egypt's Sisi Eying GCC 'Membership'
    SUBSCRIPTION SATURDAY, MAY 10, 2014 RAJAB 11, 1435 AH No: 16161 MERS death Massacres of Sharapova, toll rises to Muslims darken Nadal storm 126 in Saudi immigration into Madrid Arabia 9 debate13 in India semi-finals48 Egypt’s Sisi eying Max 40º 150 Fils GCC ‘membership’ Min 27º Sisi turns Islam on the Islamists KUWAIT: Field Marshal Abdel Fattah El-Sisi later this month, has cast himself as a defender plans to negotiate with the Gulf Cooperation of religion and taken aim at the doctrinal foun- Council (GCC) on the possibility of exempting dations of Islamist groups the state is seeking Egyptian workers from the sponsorship provi- to crush. sions, in addition to boosting military and eco- Striking a pious tone that sets him apart nomic cooperation, a Kuwaiti newspaper from former president Hosni Mubarak, Sisi also reported yesterday. Sisi’s priorities include giv- appears to be taking on the mantle of a reli- ing Egypt an observer position into the six- gious reformer. He has blamed outdated “reli- member GCC and allowing Egyptians to work gious discourse” for holding back Egypt. “I see in Saudi Arabia, Kuwait, Qatar, Bahrain, United that the religious discourse in the entire Islamic Arab Emirates and Oman (without sponsors). world has cost Islam its humanity,” Sisi said in Egypt also hopes to increase the trade and an interview televised on May 5. “This requires tourism activity with Saudi Arabia, UAE, Kuwait us, and for that matter all leaders, to review and Bahrain by eliminating visa requirements if their positions.” With references to God and Egypt becomes an observer-member of the morality, Sisi may turn out to be the most out- GCC according to a ‘high level sources’ in the wardly pious of any of the military men to have Field Marshal’s elections campaign.
    [Show full text]
  • Online Leisure Communities: the Case of Tennis Enthusiasts by Nadina Ayer a Thesis Presented to the University of Waterloo in F
    Online Leisure Communities: The Case of Tennis Enthusiasts by Nadina Ayer A thesis presented to the University of Waterloo in fulfillment of the thesis requirements for the degree of Doctor of Philosophy in Recreation and Leisure Studies Waterloo, Ontario, Canada, 2017 ©Nadina Ayer 2017 EXAMINING COMMITTEE MEMBERSHIP The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner Shannon Hebblethwaite Associate Professor Department of Applied Human Sciences Concordia University Supervisor(s) Ron McCarville Professor Department of Recreation and Leisure Studies University of Waterloo Internal Member Mark Havitz Professor Department of Recreation and Leisure Studies University of Waterloo Internal-external Member Lorne Dawson Professor Department of Sociology and Legal Studies and the Department of Religious Studies University of Waterloo Other Member(s) Luke Potwarka Associate Professor Department of Recreation and Leisure Studies University of Waterloo ii AUTHOR’S DECLARATION I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii ABSTRACT Online communities represent important virtual spaces “where people come together with others to converse, exchange information or other resources, learn, play, or just be with each other” (Resnick & Kraut, 2011, p. 1). They are communication vehicles independent of time and location (Rheingold, 1994) offering users a convenient, timely, and a reliable way to socialize with others (Chayko, 2008). As such they may replace, or at least extend more traditional communities.
    [Show full text]